Corpus ID: 237091038

# Endpoint $L^1$ estimates for Hodge systems

@inproceedings{Hernndez2021EndpointE,
title={Endpoint \$L^1\$ estimates for Hodge systems},
author={Felipe Hern{\'a}ndez and Bogdan Raiță and Daniel Spector},
year={2021}
}
• Published 16 August 2021
• Mathematics
In this paper we give a simple proof of the endpoint Besov-Lorentz estimate ‖IαF‖Ḃ0,1 d/(d−α),1 (Rd;Rk) ≤ C‖F‖L1(Rd;Rk) for all F ∈ L1(Rd;Rk) which satisfy a first order cocancelling differential constraint. We show how this implies endpoint Besov-Lorentz estimates for Hodge systems with L1 data via fractional integration for exterior derivatives.

#### References

SHOWING 1-10 OF 30 REFERENCES
Estimates for L-1 vector fields under higher-order differential conditions
We prove that an L-1 vector field whose components satisfy some condition on k-th order derivatives induce linear functionals on the Sobolev space W-1,W-n(R-n). Two proofs are provided, relying onExpand
A note on div curl inequalities
• Mathematics
• 2005
(Note: We state this result, and others below, for smooth functions or forms of compact support. More general formulations then follow by standard limiting arguments). The result above is remarkableExpand
New estimates for the Laplacian, the div-curl, and related Hodge systems
• Mathematics
• 2004
Abstract We establish new estimates for the Laplacian, the div–curl system, and more general Hodge systems in arbitrary dimension, with an application to minimizers of the Ginzburg–Landau energy. ToExpand
New Directions in Harmonic Analysis on $L^1$
The study of what we now call Sobolev inequalities has been studied for almost a century in various forms, while it has been eighty years since Sobolev's seminal mathematical contributions. Yet thereExpand
New estimates for elliptic equations and Hodge type systems
• Mathematics
• 2007
We establish new estimates for the Laplacian, the div-curl system, and more general Hodge systems in arbitrary dimension n, with data in L1. We also present related results concerning differentialExpand
Limiting Fractional and Lorentz Space Estimates of Differential Forms
We obtain estimates in Besov, Triebel-Lizorkin and Lorentz spaces of differential forms on R-n in terms of their L-1 norm.
An $L^1$-type estimate for Riesz potentials
• Mathematics
• 2014
In this paper we establish new $L^1$-type estimates for the classical Riesz potentials of order $\alpha \in (0, N)$: \[ \|I_\alpha u\|_{L^{N/(N-\alpha)}(\mathbb{R}^N)} \leq CExpand
Some remarks on L1 embeddings in the subelliptic setting
• Mathematics
• 2019
In this paper we establish an optimal Lorentz estimate for the Riesz potential in the $L^1$ regime in the setting of a stratified group $G$: Let $Q\geq 2$ be the homogeneous dimension of $G$ andExpand
Function Spaces and Potential Theory
• Mathematics
• 1995
The subject of this book is the interplay between function space theory and potential theory. A crucial step in classical potential theory is the identification of the potential energy of a chargeExpand
Two Approximation Results for Divergence Free Vector Fields
• Physics, Mathematics
• 2020
In this paper we prove two approximation results for divergence free vector fields. The first is a form of an assertion of J. Bourgain and H. Brezis concerning the approximation of solenoidal chargesExpand